1. Field of the Invention
The present invention relates to a method for analyzing a unction, a method for evaluating a semiconductor wafer, a method for evaluating an insulating film, and a Schottky junction analyzing apparatus. In particular, the present invention relates to an improved method for obtaining the electrical field dependence of the Schottky barrier height (which shows the degree of dependence of barrier height in a Schottky junction on an electrical field applied to a Schottky barrier interface).
2. Description of the Related Art
In evaluating semiconductor crystal forming a semiconductor wafer and evaluating the characteristics of a semiconductor device having a Schottky junction it is, very important to measure the barrier height in a Schottky junction formed at an interface between a semiconductor region and a Schottky electrode. As is disclosed in Japanese Laid-Open Patent Publication No. 60-207345 (Reference 1), a method for evaluating a Schottky barrier by measuring the current-voltage (I-V) or capacitance-voltage (C-V) characteristics of a Schottky junction have been widely used in the past.
In general, the I-V characteristics of a Schottky junction are given by the following Expressions (1) and (2), as is disclosed in Physics of Semiconductor Devices, 1981, John Wiley & Sons (Reference 2). EQU J=J.sub.s {exp(qV/kT)-1} (1) EQU J.sub.s =AT.sup.2 exp(-q.PHI..sub.b /kT) (2)
where J is the current flowing through a Schottky junction, J.sub.s the saturated current density, .PHI..sub.b the Schottky barrier height, q the electronic charge, V the voltage applied to the Schottky junction, k the Boltzmann's constant, T the absolute temperature (.degree.K), and A the effective Richardson constant.
According to Expression (1), when a forward bias voltage is applied to the Schottky junction, the current J flowing through the Schottky junction exponentially increases. On the other hand, when a reverse bias voltage is applied to the Schottky junction, the current J flowing through the Schottky junction is saturated at -J.sub.s.
It is common knowledge that a reverse direction current (hereinafter, referred to as a leak current) in a Schottky junction remarkably increases with the increase in a reverse bias voltage. In other words, the decrease in an effective barrier is observed. This corresponds to the Schottky barrier height .PHI..sub.b in Expression (2) varying with a reverse bias V.
Such an effective barrier lowering phenomenon is caused by a tunneling current passing through a barrier and an insulating film interposed between a Schottky electrode and a semiconductor.
First, the decrease in an effective barrier caused by a tunneling current will be described. As a leak current flowing through a Schottky junction, there is a thermionic emission current which goes over a Schottky barrier and a tunneling current which passes through the Schottky barrier. As disclosed in Solid State Electronics, June, 1976, Vol. 19, No. 6, pp. 537-543 (Reference 3), as an electrical field applied to an interface of a Schottky junction increases, the Schottky barrier height becomes lower. As a result, a tunneling current increases, and an effective barrier decreases.
Next, the decrease in an effective barrier caused by an insulating film will be described. As is disclosed in J. Appl. Phys. February, 1993, Vol. 73, No. 3, pp. 1284-1287 (Reference 4), in the case where an insulating film interposed between a Schottky electrode and a semiconductor region is thin, a barrier of the insulating film itself is negligible, and a Schottky barrier depends upon a reverse bias applied to the Schottky electrode on the insulating film. More specifically, as the reverse bias applied to the Schottky electrode increases, an electrical field generated at a Schottky junction interface increases and a Schottky barrier decreases.
As is disclosed in J. Vac. Sci. Technol., November, 1974, Vol. 11, No. 6, pp. 972-984 (Reference 5) and the above-mentioned Reference 3, the electrical field dependence of the Schottky barrier height controlled by the tunneling current and the thickness of an insulating film (i.e., the dependence of the Schottky barrier height on an electrical field strength at an interface of a Schottky junction) can be represented by the following Expression (3) with respect to the tunneling current and the insulating film. EQU .PHI..sub.b =.PHI..sub.b0 -.alpha.E (3)
where E is the electrical field strength at a Schottky junction interface, .PHI..sub.b0 the Schottky barrier height at E=0, and a the proportionality factor. As the tunneling current increases and/or as the insulating film (interposed between the Schottky electrode and the semiconductor region) at a Schottky junction interface becomes thicker, the proportionality factor .alpha. increases.
Thus, in evaluating a Schottky junction, particular, analyzing a leak current in a Schottky junction, it is required to measure the electrical field dependence of the Schottky barrier height (i.e., the proportionality factor .alpha. which determines the electrical field dependence of the Schottky barrier height).
However, it is difficult to directly measure the electrical field strength E at an interface in the above-mentioned Expression (3). Therefore, the electrical field strength at an interface is calculated by using an analytical expression (Expression (4)) of the voltage dependence of electrical field strength at an interface, whereby the proportionality factor .alpha. is extracted. The barrier height .PHI..sub.b0 (E=0) in Expression (3) can be easily obtained from the C-V characteristics with respect to the Schottky junction. The barrier height .PHI..sub.b in Expression (3) can be relatively easily obtained from the I-V characteristics and the current-temperature characteristics with respect to the Schottky junction.
More specifically, as disclosed in Reference 2, in the case where the thickness of a Schottky contact layer (i.e., a semiconductor region) is larger than that of a depletion layer, the electrical field strength at an interface of a Schottky junction can be represented by the following Expression (4). EQU E=2qN.sub.d +L /.epsilon.(V.sub.bi -V-kT/q+L ) (4)
where V.sub.bi is the built-in voltage, N.sub.d is the donor impurity density of a Schottky contact layer, and .epsilon. is the semiconductor permittivity.
As is disclosed in Appl. Phys. Lett., April, 1993 Vol. 62, No. 16, pp. 1964-1966 (Reference 6), the electrical field strength at an interface of a Schottky junction can be calculated from a voltage applied to the Schottky junction by using Expression (4), and the electrical field dependence of the Schottky barrier height (i.e., proportionality factor .alpha.) can be extracted by substituting the electrical field strength into Expression (3) together with the barrier height .PHI..sub.b and .PHI..sub.b0.
However, according to the above-mentioned method for obtaining the electrical field dependence of the Schottky barrier height, in order to calculate the electrical field strength at an interface of a Schottky junction from a bias voltage applied to the Schottky junction, Expression (4) (i.e., an analytical expression which represents the voltage dependence of the electrical field strength at an interface) is used. Therefore, values of parameters of the build-in voltage V.sub.bi and the donor impurity density of a Schottky contact layer are required. There is a possibility that the reliability of the calculated result decreases due to errors in measurement of the parameters.
Furthermore, in the case where the thickness of a Schottky contact layer is smaller than that of a depletion layer, the above-mentioned Expression (4) does not hold. Therefore, it is required to find an analytical expression which holds for this structure.
In a semiconductor wafer, having a multilayer-epi structure in which a plurality of epitaxial layers are formed, included in a high electron mobility transistor, the distribution of electrons in a depletion layer is complicated, making it difficult to derive a precise analytical expression representing the voltage dependence of electrical field strength at an interface. Thus, it was not possible to extract the electrical field dependence of the Schottky barrier height in such a device structure.